# 8.9 - 8.9(a The formulas to use are = x y i =1 n i n i nx y...

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8.9 (a) The formulas to use are 2 1 2 1 x n x y x n y x n i i n i i i = = = β ± and x y α ˆ = ± The various quantities involved are calculated in the following table: n = 3 x i y i x i y i x i 2 y i ' (y i -y i ') 2 1.05 63 66.15 1.1025 53.3363865 93.3854267 1.83 92 168.36 3.3489 107.417521 237.699949 3.14 204 640.56 9.8596 198.246093 33.1074492 Sum = 6.02 359 875.07 14.311 364.192825 Mean = 2.00666667 119.666667 Beta = 154.676667 / 2.23086667 = 69.335 Alpha = 119.666667 - 139.131807 = -19.465 The regression line y = –19.46514060 + 69.33478768 x can be plotted on the scattergram, and has the best fit to the data (in a least square sense). (b) Note the words “for given floor area”. In this case, we should not simply calculate the sample standard deviation of the y data, since although the individual y i ’s may deviate a lot from their mean, this may be due to changes in x and hence not really a randomness of y. Hence we need to calculate the conditional variance E(Y | x), assuming it is a constant. An

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8.9 - 8.9(a The formulas to use are = x y i =1 n i n i nx y...

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